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== LaTeX Equation Array == | |||
<math> | |||
\begin{eqnarray} | |||
\nonumber T & = & \int_{A}r(\tau{dA})= | |||
\int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA \\ | |||
\nonumber & = & \frac{\tau_{max}}{R}\int_{A}r^{2}dA = | |||
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{2}r{dr}{d\phi} = | |||
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{3}{dr}{d\phi} \\ | |||
\nonumber & = & | |||
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\left[\frac{r^4}{4}\right]_{r=0}^{r=R}{d\phi} | |||
= \frac{\tau_{max}}{R}\int_{0}^{2\pi}\frac{R^4}{4}{d\phi} \\ | |||
\nonumber & = & | |||
\frac{\tau_{max}}{R}\left[\frac{R^4}{4}\phi\right]_{\phi=0}^{\phi=2\pi} | |||
= \frac{\tau_{max}}{R}\times\frac{\pi{R}^4}{2} = | |||
\frac{\tau_{max}}{R}\times{J} | |||
\end{eqnarray} | |||
</math> | |||
Latest revision as of 03:32, 22 October 2024
x > y
LaTeX Equation Array
Failed to parse (unknown function "\begin{eqnarray}"): {\displaystyle \begin{eqnarray} \nonumber T & = & \int_{A}r(\tau{dA})= \int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA \\ \nonumber & = & \frac{\tau_{max}}{R}\int_{A}r^{2}dA = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{2}r{dr}{d\phi} = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{3}{dr}{d\phi} \\ \nonumber & = & \frac{\tau_{max}}{R}\int_{0}^{2\pi}\left[\frac{r^4}{4}\right]_{r=0}^{r=R}{d\phi} = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\frac{R^4}{4}{d\phi} \\ \nonumber & = & \frac{\tau_{max}}{R}\left[\frac{R^4}{4}\phi\right]_{\phi=0}^{\phi=2\pi} = \frac{\tau_{max}}{R}\times\frac{\pi{R}^4}{2} = \frac{\tau_{max}}{R}\times{J} \end{eqnarray} }